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e2-sample

# e2-sample - K = 6 × 10 8 and growth rate k = 0 6 Time is...

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Math 170, Section 01, Exam 2, Sample Monday, October 19th, 2009 Name (PRINT clearly): You will receive full credit only if you show all work and explain all steps. 1. The air in a spacecraft is initially at a ratio of 20% oxygen to 80% nitrogen. The spacecraft has volume of 100 cubic meters. There is a small leak in the spacecraft that causes the air to escape at a rate of 0.1 cubic meters per minute. A mixture of 25% oxygen to 75% nitrogen flows in to the spacecraft. (a) Let y denote the amount of oxygen in the tank. Setup a differential equation to model the amount of oxygen in the spacecraft. (b) Solve the differential equation. (c) What is the percentage of oxygen in the air after 5 minutes. (d) What happens in the long run? 2. Suppose the the population of fish in the North sea can be modelled using a logistic equation with carrying capacity
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Unformatted text preview: K = 6 × 10 8 and growth rate k = 0 . 6. Time is measured in years. (a) If the population of ﬁsh in 1999 was 2 × 10 8 , then what is the population now? (b) How long will it, or did it, take to reach 4 × 10 8 ? (c) How long will it take to reach K ? 3. Solve the following diﬀerential equations: (a) dy dt = 2-3 y 100 + 2 t , y (0) = 100 (b) xy = y + x 2 sin( x ), y ( π ) = 0 4. (a) Let a n = ne-n . Determine whether the sequence is decreasing or increasing. (b) Find the limit of the following sequences: i. a n = sin(sin( n )) √ n +1 ii. a n = sin( nπ/ 2) iii. a n = ln( n 2 + 1)-ln(3 n 2-2) 1...
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